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Fit a curve y=ax+bx2 for the data; | x : | 1 | 2 | 3 | 4 | 5 | 6 || y : | 2.51 | 5.82 | 9.93 | 14.84 | 20.55 | 27.06 |

written 4.6 years ago by teamques10 ★ 70k

modified 4.0 years ago by pg1118329 • 0

engineering mathematics

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1 Answer

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written 4.6 years ago by teamques10 ★ 70k

x	1	2	3	4	5	6	21
y	2.51	5.82	9.93	14.48	20.55	27.06	80.35
x2	1	4	9	16	25	36	91
xy	2.51	11.64	29.79	57.92	102.75	162.36	366.97
x3	1	8	27	64	125	216	441

$y=ax+bx^2 \\ \sum y =a \sum x + b \sum x^2 \\ 80.35 = 21a+91b \ \cdots (A)$

Also,

$xy=ax^2+bx^3$

$\sum xy = a \sum x^2 + b \sum x^3$

$366.97=91a+441b \ \cdots (B)$

Solving (A) and (B) simultaneously,

$a\approx 2, \ b\approx 0.4$

Hence, the required curve for the given data is

$y=2x+0.4x^2$

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